astronomical unit (AU, or au) | unit of measurement | Britannica.com Astronomical unit (AU, or au) unit of measurement parsec Astronomical unit (AU, or au), a unit of length effectively equal to the average, or mean, distance between Earth and the Sun , defined as 149,597,870.7 km (92,955,807.3 miles). Alternately, it can be considered the length of the semimajor axis—i.e., the length of half of the maximum diameter—of Earth’s elliptical orbit around the Sun. The astronomical unit provides a convenient way to express and relate distances of objects in the solar system and to carry out various astronomical calculations. For example, stating that the planet Jupiter is 5.2 AU (5.2 Earth distances) from the Sun and that Pluto is nearly 40 AU gives ready comparisons of the distances of all three bodies.

Comparative data for the Sun, planets, and other solar system objects object (average, except where ranges are given) mean density (g/cm3) inclination of equator to orbit (obliquity; in degrees) AU* 2-4.5 (main and outer belts) 300-600 5-30 (mainly between orbits of Jupiter and Neptune) 750-4,490 total possibly as much as 0.5 -- -- -- *One astronomical unit (AU) is the mean distance of Earth from the Sun, about 150 million km. **R following the quantity indicates retrograde rotation. In principle, the easiest way to determine the value of the astronomical unit would have been to measure the Earth-Sun distance directly by means of the parallax method. In this approach, two observers stationed at the ends of a long, accurately known baseline—ideally, a baseline as long as Earth’s diameter—would simultaneously record the position of the Sun against the essentially motionless background of the distant stars . Comparison of the observations would reveal an apparent shift, or angular (parallax) displacement, of the Sun against the remote stars.

A simple trigonometric relationship incorporating this angular value and the baseline length then could be used to find the Earth-Sun distance. In practice, however, the method cannot be applied, because the Sun’s intense glare blots out the background stars needed for the parallax measurement . By the 17th century astronomers understood the geometry of the solar system and the motion of the planets well enough to develop a proportional model of objects in orbit around the Sun, a model that was independent of a particular scale. To establish the scale for all orbits and to determine the astronomical unit, all that was needed was an accurate measurement of the distance between any two objects at a given instant. In 1672 the Italian-born French astronomer Gian Domenico Cassini made a reasonably close estimate of the astronomical unit based on a determination of the parallax displacement of the planet Mars —and thus its distance to Earth. Later efforts made use of widely separated observations of the transit of Venus across the Sun’s disk to measure the distance between Venus and Earth.

Similar Topics "Astronomical Unit," or Earth-Sun Distance, Gets an Overhaul - Scientific American Scientific American Space "Astronomical Unit," or Earth-Sun Distance, Gets an Overhaul A new AU redefinition involves changing it to a single number rather than basing it on a somewhat baffling equation By Geoff Brumfiel on September 14, 2012 Credit: NASA Mars Exploration Program Advertisement | Report Ad By Geoff Brumfiel of Nature magazine Without fanfare, astronomers have redefined one of the most important distances in the Solar System. The astronomical unit (au) — the rough distance from the Earth to the Sun — has been transformed from a confusing calculation into a single number. The new standard, adopted in August by unanimous vote at the International Astronomical Union's meeting in Beijing, China, is now 149,597,870,700 meters — no more, no less. The effect on our planet’s inhabitants will be limited. The Earth will continue to twirl around the Sun, and in the Northern Hemisphere, autumn will soon arrive. But for astronomers, the change means more precise measurements and fewer headaches from explaining the au to their students.

The distance between the Earth and the Sun is one of the most long-standing values in astronomy. The first precise measurement was made in 1672 by the famed astronomer Giovanni Cassini, who observed Mars from Paris, France, while his colleague Jean Richer observed the planet from French Guiana in South America. Taking the parallax, or angular difference, between the two observations, the astronomers calculated the distance from Earth to Mars and used that to find the distance from the Earth to the Sun. Their answer was 140 million kilometers — not far off from today’s value. Until the last half of the twentieth century, such parallax measurements were the only reliable way to derive distances in the Solar System, and so the au continued to be expressed as a combination of fundamental constants that could transform angular measurements into distance. Most recently, the au was defined as (take a deep breath): “the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day (known as the Gaussian constant)”.

The definition cheered fans of German mathematician Carl Friedrich Gauss, whose constant sits at the heart of the whole affair, but it caused trouble for astronomers. For one thing, it left introductory astronomy students completely baffled, says Sergei Klioner, an astronomer at the Technical University of Dresden in Germany. But, more importantly, the old definition clashed with Einstein’s general theory of relativity. As its name implies, general relativity makes space-time relative, depending on where an observer is located. The au, as formerly defined, changed as well. It shifted by a thousand meters or more between Earth’s reference frame and that of Jupiter’s, according to Klioner. That shift did not affect spacecraft, which measure distance directly, but it has been a pain for planetary scientists working on Solar System models. The Sun posed another problem. The Gaussian constant is based on Solar mass, so the au was inextricably tied to the mass of the Sun. But the Sun is losing mass as it radiates energy, and this was causing the au to change slowly as well. The revised definition wipes away the problems of the old au.

A fixed distance has nothing to do with the Sun’s mass, and the meter is defined as the distance traveled by light in a vacuum in 1 / 299,792,458 of a second. Because the speed of light is constant in all reference frames, the au will no longer change depending on an observer’s location in the Solar System. Redefining the au has been possible for decades — modern astronomers can use spacecraft, radars and lasers to make direct measurements of distance. But “some of them thought it was a little bit dangerous to change something,” says Nicole Capitaine, an astronomer at the Paris Observatory in France. Some feared the change might disrupt their computer programs, others held a sentimental attachment to the old standard. But after years of lobbying by Capitaine, Klioner and others, the revised unit has finally been adopted. Capitaine and Klioner say that the streamlined au is already having a positive impact on their lives. Lobbying for the change has been time-consuming, Capitaine says: “I will have more time to devote to my research.” “I'm happy that I don't have to explain it to my students any longer,” adds Klioner.

The new definition “is much easier to understand now for everybody.” This article is reproduced with permission from the magazine Nature . The article was first published on September 14, 2012. Advertisement | What is an astronomical unit? | Space | EarthSky What is an astronomical unit? By Bruce McClure in Space | October 21, 2016 Astronomers use astronomical units – or AU – to describe solar system distances. Definition of AU here. Also, mean distances in AU to prominent solar system objects. Artist’s concept of Earth and sun. One astronomical unit = the average distance between them. Image via NASA . 2017 EarthSky Lunar Calendar pre-sale…is happening NOW! Astronomers like to list the distances to objects within our solar system (planets, dwarf planets, asteroids, comets, spacecraft, etc.) in terms of an astronomical unit. How far is that? Follow the links below to learn more about this basic distance unit in our solar system. Definition of astronomical unit. For general reference, we can say that one astronomical unit (AU) represents the mean distance between the Earth and our sun. An AU is approximately 93 million miles (150 million km).

It’s approximately 8 light-minutes. More exactly, one astronomical unit (AU) = 92,955,807 miles (149,597,871 km). Earth’s orbit around the sun isn’t a perfect circle. So Earth’s distance from the sun changes throughout the year. Astronomers give the Earth’s changing distance throughout the year relative to the astronomical unit, too. For instance, when the Earth is at perihelion – its nearest point to the sun for the year, in January – it’s about 0.983 AU from the sun. When our planet swings out to aphelion – its farthest point, in July – we’re about 1.017 AU away from the sun. Distances from the sun of planets in our solar system, expressed in A.U. Graph via planetsforkids.org Mean distance ( semi-major axis ) from sun to each planet, in AU. Mercury: 0.387 AU Source: Planetary Fact Sheet If you want to find out the distances of the solar system planets from the Earth and sun right now, click here or here .

Artist’s concept of the dwarf planet Eris, whose distance from the sun varies from 38.255 to 97.661 au. Image via HubbleSite Mean distance from sun to some dwarf planets, in AU. Ceres: 2.767 AU Eris: 67.958 AU Sedna: 518.57 AU Artist’s rendering of the Kuiper Belt and the Oort Cloud, the distant icy realm of the solar system. Image via NASA Mean distance to Kuiper Belt, farthest spacecraft, Oort Cloud, in AU. Oort Cloud : 5,000 to 100,000 AU Largest circle with yellow arrow indicates one light year from our sun. Smallest yellow sphere is one light-week. Larger yellow sphere is one light-month. Read more about this image at Wikimedia Commons. Amount of distance in a light-year, in AU One light-year = 63,240 AU Bottom line: Astronomers like to list the distances to objects within our solar system (planets, dwarf planets, asteroids, comets, spacecraft, etc.) in terms of the astronomical unit, or AU.

One astronomical unit is the approximate mean distance between the Earth and sun. It’s about 93 million miles (150 million km), or 8 light-minutes. Astronomical Units - One Universe at a Time One Universe at a Time In Solar System by Brian Koberlein 14 April 2014 0 Comments Yesterday I wrote about how astronomers can use the principle of parallax to measure the distance to stars . However this principle was first applied to the moon and the planets. More than 2,000 years ago Hipparchus used the parallax of the moon to measure its distance. He found that the distance to the moon was about 60 times the radius of the Earth, or about 237,000 miles. (The actual average distance is 239,000 miles.) Earlier, Aristarchus measured the angle between the Moon and the Sun when the Moon was in its quarter phase (when half of it is illuminated from the Sun), and used trigonometry to determine that the Sun was about 20 times further away than the Moon, or about 4,740,000 miles.

This distance is much lower than its actual value, but was the accepted value until at least the 1400s. Despite their success with the Moon and the Sun, the distances to the planets were essentially unknown. It was known, for example that Mercury and Venus must be closer than the Sun, since they occasionally passed in front of (or transitted) the Sun. The other known planets, (Mars, Jupiter and Saturn) never transited the Sun, and so they must be farther away. But at the time astronomers didn’t have the necessary tools to measure planetary distances accurately. This was further complicated by the fact that until the 1500s it was generally thought that the Sun, Moon and planets moved around the Earth, which was fixed at the center of the universe. It was not until Copernicus published his heliocentric (sun-centered) view of the universe that astronomers could finally determine the size of our solar system. By the early 1600s, Johannes Kepler was able to demonstrate how the distances of the planets were directly related to the distance from the Earth to the Sun. Using precise measurements made by Tycho Brahe he devised three laws of planetary motion, which are now known as Kepler’s Laws.

One of these laws stated that the period of a planet’s motion (how long it takes to orbit the Sun) is related to the semi-major axis of its orbit (essentially its average distance from the Sun). By determining a planet’s orbital period in Earth years, astronomers could easily calculate distance from the Sun as it relates the distance from the Earth to the Sun. This meant astronomers could define the distance from the Earth to the Sun as one astronomical unit (1 au). Thus, Venus was 0.72 au from the Sun, Jupiter was 5.2 au, Saturn was 9.5 au, and so on. But this only gave the proportional distance. To find the actual distances of the planets, astronomers needed an accurate measurement of 1 au. In Kepler’s time no one had such a measurement. Kepler thought the distance was at least three times greater than the distance measured by Aristarchus, but wasn’t able to make an accurate measurement. Then in 1769, astronomers finally had the opportunity to undertake an accurate measurement. In June of that year Venus would transit the Sun, and astronomers now had clocks and telescopes of sufficient accuracy.

Several teams of astronomers were sent across the globe, including one to Tahiti by James Cook. The astronomer William Hirst wrote of his measurements of the transit in a letter to the Royal Society. Hisrt’s observations were like those of many other astronomers, in that he measured the times at which the transit of Venus began and ended as seen from his location. By comparing his measurements with those of other astronomers, it was possible to determine the parallax of Venus, and therefore determine its distance. The exact timing of the transit was hampered by the fact that Venus would appear somewhat distorted when it was near the edge of the sun, which is known as the black drop effect. You can see this in Hirst’s sketches seen below. Still, by 1771 several different measurements were collected and analyzed. The result was that the distance Sun was 24,000 Earth radii, or about 95 million miles. This is slightly larger than the actual value of 93 million miles, but is significantly more accurate that of Aristarchus. Astronomers now had a reasonable measurement of the solar system. Sketches of the transit of Venus. Credit: W.

Hirst Planetary distances can now be measured with radio telemetry to an accuracy of 3 parts in a billion. It is accurate enough to observe it changing over time. The Sun gradually loses mass as it radiates energy, and so the orbits of the planets (including Earth) are slowly getting larger. Thus the astronomical unit is increasing by several meters per century. In 2012, the International Astronomical Union defined the astronomical unit as a fixed standard, which means the Earth’s distance is slowly getting larger than an astronomical unit. But thanks to a rare alignment of planets 250 years ago, we were able to learn for the first time just how large our solar system really is. Related Posts Astronomical unit | Wiki | Everipedia × Want to change something on this page or create your own? Register today, it's fast and free. Astronomical unit 1 au, AU or ua in ... ... is equal to ...

7011149596734827110♠4.8481×10−6 pc 7011149602530962920♠1.5813×10−5 ly Freebase ID EN Wikipedia URL The astronomical unit (symbol au, [2] [3] AU [4] or ua) is a unit of length , roughly the distance from Earth to the Sun . However, that distance varies as Earth orbits the Sun, from a maximum ( aphelion ) to a minimum ( perihelion ) and back again once a year. Originally conceived as the average of Earth's aphelion and perihelion, it is now defined as exactly 7011149597870700000♠149597870700 metres (about 150 million kilometres, or 93 million miles). The astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars.

However, it is also a fundamental component in the definition of another unit of astronomical length, the parsec . Symbol usage A variety of unit symbols and abbreviations are in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) used the symbol A for the AU. [5] In 2006, the International Bureau of Weights and Measures (BIPM) recommended ua as the symbol for the unit. [6] In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au". [2] In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au". [7] The symbol "AU" [4] and abbreviation a.u. are also used. In ISO 80000-3 , the symbol of the astronomical unit is "ua". Development of unit definition Earth's orbit around the Sun is an ellipse . The semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion.

The centre of the sun lies on this straight line segment, but not at its midpoint. Because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, and made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax (apparent shifts of position) in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated. But all measurements are subject to some degree of error or uncertainty, and the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances. Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became increasingly precise and sophisticated, and ever more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics , which govern the motions of objects in space.

The expected positions and distances of objects at an established time are calculated (in AU) from these laws, and assembled into a collection of data called an ephemeris . NASA 's Jet Propulsion Laboratory provides one of several ephemeris computation services. [8] In 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition . Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides. It stated that "the astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value 6998172020989500000♠0.01720209895 when the units of measurement are the astronomical units of length, mass and time".

[5] [9] [10] Equivalently, by this definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of 6998172020989500000♠0.01720209895 radians per day; or alternatively that length for which the heliocentric gravitational constant (the product GM☉) is equal to (6998172020989500000♠0.01720209895)2 AU3/d2, when the length is used to describe the positions of objects in the Solar System. Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry . As with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object.

Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is basically the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting. In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in the TDB scale leads to a value for the speed of light in astronomical units per day (of 7004864000000000000♠86400 s). By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at 7008299792458018110♠173.1446326847(69) AU/d (TDB).

[12] In 1983, the International Committee for Weights and Measures (CIPM) modified the International System of Units (SI, or "modern" metric system) to make the metre independent of physical objects entirely, because other measurements had become too precise for reference to the prototype platinum metre to remain useful. Instead, the metre was redefined in terms of the speed of light in vacuum, which could be independently determined at need. The speed of light could then be expressed exactly as c0 = 7008299792458000000♠299792458 m/s, a standard also adopted by the IERS numerical standards. [14] From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be τA = 7002499004783806100♠499.0047838061±0.00000001 s, more than 8 minutes.

By simple multiplication then, the best IAU 2009 estimate was A = c0τA = 7011149597870700000♠149597870700±3 m, [17] based on a comparison of JPL and IAA–RAS ephemerides. [18] [21] [22] In 2006, the BIPM reported a value of the astronomical unit as 7011149597870691000♠1.49597870691(6)×1011 m. [6] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 7011149597870700000♠149597870700 m.

[7] This estimate was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers. In 2012, finding that the equalization of relativity alone would make the definition overly complex, the IAU simply used the 2009 estimate to redefine the astronomical unit as a conventional unit of length directly tied to the metre (exactly 7011149597870700000♠149597870700 m). [17] [23] The new definition also recognizes as a consequence that the astronomical unit is now to play a role of reduced importance, limited in its use to that of a convenience in some applications.

[17] 1 astronomical unit ≈ 7000484813680000000♠4.8481368 millionths of a parsec ≈ 7001158125070000000♠15.812507 millionths of a light-year This definition makes the speed of light, defined as exactly 7008299792458000000♠299792458 m/s, equal to exactly 7008299792458000000♠299792458 × 7004864000000000000♠86400 ÷ 7011149597870700000♠149597870700 or about 7002173144632674240♠173.144632

674240...

AU/d, some 60 parts per trillion less than the 2009 estimate. Usage and significance With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant , that is the product of the gravitational constant G and the solar mass M☉ . Neither G nor M☉ can be measured to high accuracy in SI units, but the value of their product is known very precisely from observing the relative positions of planets ( Kepler's Third Law expressed in terms of Newtonian gravitation). Only the product is required to calculate planetary positions for an ephemeris , so ephemerides are calculated in astronomical units and not in SI units. The calculation of ephemerides also requires a consideration of the effects of general relativity . In particular, time intervals measured on Earth's surface ( terrestrial time , TT) are not constant when compared to the motions of the planets: the terrestrial second (TT) appears to be longer during the Northern Hemisphere winter and shorter during the Northern Hemisphere summer when compared to the "planetary second" (conventionally measured in barycentric dynamical time , TDB).

This is because the distance between Earth and the Sun is not fixed (it varies between 6999983289891200000♠0.9832898912 and 7011152097701010286♠1.0167103335 AU) and, when Earth is closer to the Sun ( perihelion ), the Sun's gravitational field is stronger and Earth is moving faster along its orbital path . As the metre is defined in terms of the second and the speed of light is constant for all observers, the terrestrial metre appears to change in length compared to the "planetary metre" on a periodic basis. The metre is defined to be a unit of proper length , but the SI definition does not specify the metric tensor to be used in determining it. Indeed, the International Committee for Weights and Measures (CIPM) notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored". As such, the metre is undefined for the purposes of measuring distances within the Solar System.

The 1976 definition of the astronomical unit was incomplete because it did not specify the frame of reference in which time is to be measured, but proved practical for the calculation of ephemerides: a fuller definition that is consistent with general relativity was proposed, [24] and "vigorous debate" ensued [25] until in August 2012 the IAU adopted the current definition of 1 astronomical unit = 7011149597870700000♠149597870700 metres . The astronomical unit is typically used for stellar system scale distances, such as the size of a protostellar disk or the heliocentric distance of an asteroid, whereas other units are used for other distances in astronomy . The astronomical unit is too small to be convenient for interstellar distances, where the parsec and light year are widely used. The parsec (parallax arcsecond) is defined in terms of the astronomical unit, being the distance of an object with a parallax of 1 arcsecond . The light year is often used in popular works, but is not an approved non-SI unit and is rarely used by professional astronomers.

[26] History According to Archimedes in the Sandreckoner (2.1), Aristarchus of Samos estimated the distance to the Sun to be 7004100000000000000♠10000 times Earth's radius (the true value is about 7004230000000000000♠23000). [27] However, the book On the Sizes and Distances of the Sun and Moon , which has long been ascribed to Aristarchus, says that he calculated the distance to the Sun to be between 18 and 20 times the distance to the Moon , whereas the true ratio is about 389.174. The latter estimate was based on the angle between the half moon and the Sun, which he estimated as 87° (the true value being close to 89.853°).

Depending on the distance that Van Helden assumes Aristarchus used for the distance to the Moon, his calculated distance to the Sun would fall between 380 and 7003152000000000000♠1520 Earth radii.

According to Eusebius of Caesarea in the Praeparatio Evangelica (Book XV, Chapter 53), Eratosthenes found the distance to the Sun to be "σταδιων μυριαδας τετρακοσιας και οκτωκισμυριας" (literally "of stadia myriads 400 and 7004800000000000000♠80000" but with the additional note that in the Greek text the grammatical agreement is between myriads (not stadia) on the one hand and both 400 and 7004800000000000000♠80000 on the other, as in Greek, unlike English, all three (or all four if one were to include stadia) words are inflected .

This has been translated either as 7006408000000000000♠4080000 stadia (1903 translation by Edwin Hamilton Gifford ), or as 7008804000000000000♠804000000 stadia (edition of Édouard des Places, dated 1974–1991). Using the Greek stadium of 185 to 190 metres, [29] [30] the former translation comes to 7008754800000000000♠754800 km to 7008775200000000000♠775200 km, which is far too low, whereas the second translation comes to 148.7 to 152.8 million kilometres (accurate within 2%).

[31] Hipparchus also gave an estimate of the distance of Earth from the Sun, quoted by Pappus as equal to 490 Earth radii. According to the conjectural reconstructions of Noel Swerdlow and G. J. Toomer , this was derived from his assumption of a "least perceptible" solar parallax of 7 arc minutes. [32] A Chinese mathematical treatise, the Zhoubi suanjing (c. 1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places 7003100000000000000♠1000 li apart and the assumption that Earth is flat. Distance to the Sun 1.0000 Sources: In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 7003121000000000000♠1210 times Earth's radius .

[34] To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of 641/6 Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be 7003121000000000000♠1210 Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure.

Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few percent can make the solar distance infinite. After Greek astronomy was transmitted to the medieval Islamic world, astronomers made some changes to Ptolemy's cosmological model, but did not greatly change his estimate of the Earth–Sun distance. For example, in his introduction to Ptolemaic astronomy, al-Farghānī gave a mean solar distance of 7003117000000000000♠1170 Earth radii, whereas in his zij , al-Battānī used a mean solar distance of 7003110800000000000♠1108 Earth radii. Subsequent astronomers, such as al-Bīrūnī , used similar values.

Later in Europe, Copernicus and Tycho Brahe also used comparable figures (7003114200000000000♠1142 and 7003115000000000000♠1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for Earth (which could then be applied to the other planets). The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye. Flemish astronomer Godefroy Wendelin repeated Aristarchus' measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven.

A somewhat more accurate estimate can be obtained by observing the transit of Venus . [35] By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the solar parallax α (which cannot be measured directly [36] ). Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15 arcseconds , similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by A . {displaystyle A={cot alpha }.} The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of 15" is equivalent to an Earth–Sun distance of 7004137500000000000♠13750 Earth radii.

Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars , he estimated a value of about 7004240000000000000♠24000 Earth radii, [37] equivalent to a solar parallax of 8.6". Although Huygens' estimate is remarkably close to modern values, it is often discounted by historians of astronomy because of the many unproven (and incorrect) assumptions he had to make for his method to work; the accuracy of his value seems to be based more on luck than good measurement, with his various errors cancelling each other out. Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 91/2", equivalent to an Earth–Sun distance of about 7004220000000000000♠22000 Earth radii.

They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 7003326900000000000♠3269 thousand toises . Another colleague, Ole Rømer , discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by James Gregory and published in his Optica Promata (1663). It was strongly advocated by Edmond Halley [39] and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation.

Despite the Seven Years' War , dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. [40] The various results were collated by Jérôme Lalande to give a figure for the solar parallax of 8.6″. Date 149.597 870 700 0.000 000 003 Another method involved determining the constant of aberration . Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80″ for the solar parallax (close to the modern value of 7000879414300000000♠8.794143″), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with A. A. Michelson to measure the speed of light with Earth-based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in kilometres.

Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant ) were incorporated into the first international system of astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. [41] The name "astronomical unit" appears first to have been used in 1903. [42] The discovery of the near-Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. [44] Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. [36] Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another.

[45] Developments The unit distance A (the value of the astronomical unit in metres) can be expressed in terms of other astronomical constants : A 2 {displaystyle A^{3}={frac {GM_{odot }D^{2}}{k^{2}}}} where G is the Newtonian gravitational constant , M☉ is the solar mass , k is the numerical value of Gaussian gravitational constant and D is the time period of one day. The Sun is constantly losing mass by radiating away energy, [47] so the orbits of the planets are steadily expanding outward from the Sun. This has led to calls to abandon the astronomical unit as a unit of measurement. [48] As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant k is fixed in the astronomical system of units , measuring the light time per unit distance is exactly equivalent to measuring the product GM☉ in SI units. Hence, it is possible to construct ephemerides entirely in SI units, which is increasingly becoming the norm.

A 2004 analysis of radiometric measurements in the inner Solar System suggested that the secular increase in the unit distance was much larger than can be accounted for by solar radiation, +7001150000000000000♠15±4 metres per century. [51] [54] The measurements of the secular variations of the astronomical unit are not confirmed by other authors and are quite controversial. Furthermore, since 2010, the astronomical unit is not yet estimated by the planetary ephemerides. [58] Examples The following table contains some distances given in astronomical units. It includes some examples with distances that are normally not given in astronomical units, because they are either too short or far too long. Distances normally change over time. Examples are listed by increasing distance. Object How is distance measured in astronomical units? | Socratic How is distance measured in astronomical units? Start with a one sentence answer Then teach the underlying concepts Don't copy without citing sources Write a one sentence answer... Answer: I want someone to double check my answer Describe your changes (optional) 200 Cancel 1 AU is the distance from the Sun to the Earth .

Explanation: 1 Astronomical Unit is taken as the Standard distance from the Sun to the Earth which is also the Semi-major axis of the Earth's orbit around the Sun, roughly equal to 1.5 million km. So, for larger distances it is preferred to use AU instead of km and for even larger distances we have Light-years and Parsecs respectively. Was this helpful? Let the contributor know! Yes Earth-Sun Distance Measurement Redefined Earth-Sun Distance Measurement Redefined By Nola Taylor Redd, Space.com Contributor | September 24, 2012 12:17pm ET MORE The astronomical unit once relied on a mathematical equation to provide its value for the distance from the Earth to the Sun. Credit: The SOHO-EIT Consortium One of the stalwart units of astronomy just got a makeover. The International Astronomical Union, the authority on astronomical constants, has voted unanimously to redefine the astronomical unit, the conventional unit of length based on the distance between the Earth and the sun.

"The new definition is much simpler than the old one," says Sergei Klioner of the Technical University of Dresden in Germany, one of a group of scientists who worked decades toward the change, which took effect last month during an IAU meeting Under the new definition, the astronomical unit (or AU) — the measurement used for the Earth-sun distance — is no longer always in flux, depending on the length of a day and other changing factors. It is now a fixed number: 149,597,870,700 meters, which is the equivalent of almost 92.956 million miles. Klioner explained the simpler definition is helpful, for instance, for scientists who formulate ephemerides — tables that give the precise position of astronomical objects in the sky. They utilize the astronomical unit to calculate the motion of bodies in the solar system. [ Solar System Explained From the Inside Out (Infographic) ] "The broader community of astronomers are able now to better, with less efforts, understand what their colleagues — astronomers who are experts in planetary ephemerides — do and how they produce the high-accuracy theories of motion in the solar system ," he told SPACE.com by email.

The revision also makes the unit easier for engineers, software designers and students to understand, Klioner and his colleague Nicole Capitaine, of Paris Observatory, noted. At the same time, the redefinition can serves an epitaph to the bygone era when Earth-bound scientists depended on viewing angles to calculate celestial distances. An established unit Lacking precise instrumentation, early astronomers relied heavily on angles to calculate the size of the universe. By studying Mars from two separate points on Earth, 17th-century Italian astronomer Giovanni Cassini was able to use trigonometry to calculate the distance from Earth to the sun with only about a 6 percent error. "Expressing distances in the astronomical unit allowed astronomers to overcome the difficulty of measuring distances in some physical unit," Capitaine told SPACE.com by email. "Such a practice was useful for many years, because astronomers were not able to make distance measurements in the solar system as precisely as they could measure angles." Modern instruments can come within a few meters of exactly determining distances of nearly150 billion meters (150 million kilometers), or some 93 million miles.

The astronomical unit eventually came to be defined by a mathematical expression that involved the mass of the sun , the length of a day, and a fixed number known as the Gaussian gravitational constant. Because the Earth orbits its star in an ellipse rather than a circle, the length of a day shifts over the course of a year. At the same time, the sun is constantly transforming mass into energy. In the 20th century, famed scientist Albert Einstein added general relativity to the mix. According to the famous theory, space-time is relative depending on one's frame of reference. The new fixed number is the best estimate of the original expression, Klioner said. "If we would decide to continue with the old definition, we would have to add several additional conventions to make the latter meaningful in the framework of general relativity," he explained. "A better way was to change the definition completely — and this is what we succeeded in doing." Capitaine said, "The change of definition of the astronomical unit mainly concerns those in the field of high-accuracy solar system dynamics." Satellites and other crafts traveling in space are not affected, because they rely on set distances.

"The distance between the Earth and the sun , as any physical distance, should be measured and cannot be fixed by any sort of resolution," Klioner said. The times, they are a-changing Capitaine and Klioner are among several scientists who worked over the last two decades on a revision of the astronomical unit. Capitaine said she first got involved when she gave a presentation in 1994 with Bernard Guinot, also of Paris Observatory. Over the course of 10 years, several published papers by various scientists discussed the ramifications of changing the stalwart unit. The three scientists presented the issue to the astronomical community on a number of different occasions. Other astronomers helped to demonstrate the feasibility of the change before it landed on the table of one of the working groups for the International Astronomical Union. The resolution was reworked several times before it won unanimous passage. "The change as we have it now is really a product of collective work," Klioner said.

He went on to add, "I think that the energy, commitment, and the worldwide scientific reputation of Nicole Capitaine were crucial for getting this change through." Shifting from a constantly changing value to a fixed number may seem like an easy choice, but the group faced some resistance. Some believed that the overhaul would be too difficult to implement with crucial software, while others were concerned that discrepancies might be introduced into past work. Still others were uncomfortable changing such a historic definition. Eventually, all concerns were apparently met. "Within the last two years, I have not heard a single objection for the change itself," Klioner said. Editor's note: This story has been corrected to fix a units error in the tenth paragraph that incorrectly stated the Earth-sun distance was nearly 150 million meters. It is nearly 150 billion meters. Follow SPACE.com on Twitter @Spacedotcom . We're also on Facebook & Google+ . Editor's Recommendations

Question: An Astronomical Unit is a standard measurement taken from the earth to where?
Answer: THE SUN